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"Due to the extremely dangerous security situation, consular assistance is no longer available within Syria.

"Australians who become involved in overseas conflicts are putting their own lives in mortal danger.

"Any Australians fighting with non-state militia in Syria or Iraq should end their involvement in the conflict now and leave the conflict zone.

"Australians are strongly advised not to travel to Syria or Iraq; any Australians in either country should leave immediately.

Kurdish fighters claim to have pushed ISIL militants out of the Syrian town of Kobane. (AAP) (AAP)

Syrian Observatory for Human Rights had reported the fighter's death on Tuesday, but was unable to confirm his nationality until now.

"An Australian man was killed in an assault on Tuesday by the Islamic State against a position of the Kurdish People's Protection Units (YPG) near Tal Hamis in Hasakeh province," Observatory director Rami Abdel Rahman said.

"Dozens of Westerners have joined the YPG's ranks.

“There are foreigners fighting on all sides of Syria's war.”

The report led to increased concern for the welfare of Northern Territory Labor figure Matthew Gardiner, who left Australia in January and is believed to have gone to Syria to support Kurdish forces in their fight against ISIL.

Mr Gardiner is a trained nurse and the ABC reported that he is believed to be in the area of the Hasakeh province providing medical assistance to the soldiers.

He has not made contact with the media since his disappearance.

Former NT Labor president and United Voice secretary Matthew Gardiner. ()

Following reports Mr Gardiner had joined the fight against ISIL, Attorney-General George Brandis reaffirmed that joining the conflict on either side was illegal.

“If you fight illegally in overseas conflicts, you face up to life in prison upon your return to Australia,” a spokesperson for Mr Brandis said.

“It is illegal to fight in Syria for either side of the conflict. It is illegal to fight for a terrorist organisation anywhere, including in Iraq.”